Newly qualified police officers in Hendon, north London. Forces must make £1.5bn savings as a result of a 20% grant cut. Photograph: Stefan Rousseau/PA

Police forces across England and Wales face making deeper spending cuts after Whitehall's spending watchdog identified a £500m "black hole" in their plans to meet their required savings targets as part of the government's austerity programme.

The National Audit Office (NAO) says police forces have so far managed to identify savings of only £1bn out of the £1.5bn required to meet their Treasury targets by 2014-15.

The report, published on Thursday, says two-thirds of forces have failed to meet their targets for cuts. Some had planned for only three years' savings instead of four, while the published plans of others "simply did not yield sufficient savings".

Her Majesty's Inspectorate of Constabulary warned last summer that the existing cuts plans drawn up as a result of a 20% real-terms cut in Whitehall grants would lead to the loss of more than 34,000 police jobs, including those of 16,200 warranted police officers. A renewed round of spending cuts could lead to further job losses.

Margaret Hodge, chair of the Commons public accounts committee, said: "I'm deeply concerned that, in 2011, two-thirds of police forces did not have realistic plans to deal with the impending cost reductions – with a shortfall of £500m. The Home Office needs to assure us as soon as possible that our police services will not suffer."

The NAO report on the financial management of the Home Office says that by the summer of 2011, 17 of the 43 forces had drawn up plans to generate the necessary cost savings, but a further 26 forces still needed to find significant extra savings.

The Whitehall auditors voice concerns that some forces still do not have the necessary expertise to best decide how and where to make savings. They say this lack of expertise and the abolition of Whitehall targets for the police forces means it is becoming increasingly difficult for the Home Office to assess whether they will meet the spending targets and do so while protecting frontline services.

They say that the introduction of police and crime commissioners and the disbandment of the Audit Commission will add to the difficulties.

The Home Office has told the Whitehall auditors it believes most of the £500m savings gap has been covered by plans drawn up by police forces since last summer. But the NAO says that cannot be confirmed until the official police inspectorate reports again later this year.

A Home Office spokesman said the funding settlement for the police waschallenging but manageable and savings could be made whilst protectingfrontline services.

"HMIC made clear last July that forces were putting plans in place toidentify the necessary savings. We are confident the gap is closingand the HMIC will report later this year on the progress being made,"he said.

But Yvette Cooper, the shadow home secretary, said the £500m shortfall in planned savings was why 16,000 police officers were being lost in England and Wales.

"We have warned for some time that police forces face serious funding gaps because of the Tory-led government's policies.

"The home secretary chose to cut police budgets by 20%, or £2bn rather than the £1bn supported by Labour and independent police experts. And by demanding the steepest cuts in the first few years, the government has made it extremely difficult for chief constables to plan sustainable savings over time," said Cooper.

"As the Home Office are clearly aware of the damage they are causingthe home secretary should urgently rethink. More and more frontlinepolice officers will be lost, and services will suffer, because ofthese cuts that go too far and too fast."